In a small bowl whisk together the olive oil, lemon juice, dijon and garlic until combined. Season to taste with salt and set aside.

Bring a medium pot of salted water to a boil over high heat. Add the green beans and potatoes to the boiling water. Cook the green beans until bright green and tender, about 2 minutes. Remove with tongs to a bowl of ice water until chilled then drain and set aside.

Continue to boil the potatoes until tender, about 15 minutes. Use a slotted spoon to remove the potatoes to a strainer and return the pot to heat. Add the vinegar and bring the water to a bare simmer.

Create a clockwise swirling motion with a ladle to create a whirlpool then carefully crack each egg individually into the pot, being careful to space them out. Cook until the whites are just set and the yolk is runny, about 3 minutes. Use a slotted spoon to remove the eggs and set them aside on a plate.

In a medium bowl toss the potatoes and green beans with half the dressing. Add the shallots, chives, dill, parsley and continue to toss.

Add the radish, arugula and the remaining vinaigrette then toss and divide among serving plates. Top with a poached egg and serve.